Quasiparticles of the υ=5/2 fractional quantum Hall (FQH) state are known as Ising anyons. Evidence supporting the υ=5/2 FQH state having non-Abelian anyons described by the Ising anyon model may be found, for example, at R. L. Willett, et al., Measurement Of Filling Factor 5/2 Quasiparticle Interference: Observation Of Charge e/4 And e/2 Period Oscillations, and W. Bishara, et al., The Non-Abelian Interferometer, copies of which are provided in the Appendix hereof, and the disclosures of which are incorporated herein by reference.
Though Ising anyons obey non-Abelian statistics, they do not have computationally universal braiding. That is, braiding transformations alone cannot generate a computationally universal gate set. Thus, in order to use them for quantum computation, it would be desirable to supplement the usual topologically-protected gates, which may be obtained either by braiding anyons or by using measurement-only anyonic quantum computation to generate braiding transformations without moving computational anyons. Measurement-only anyonic quantum computation is described and claimed in U.S. patent application Ser. No. 12/187,850, the disclosure of which is incorporated herein by reference.
It is well known that Ising anyons allow for the so-called “Clifford group” of gates to be implemented in a topologically-protected manner. However, the full set of Clifford gates cannot be obtained using only braiding operations for a given encoding of qubits in an Ising anyon. If one could switch between encodings, then one would be able to obtain all the Clifford gates. For example, entangling gates cannot be obtained via braiding operations when one qubit is encoded in four anyons, whereas if two qubits are encoded in six anyons, then entangling gates can be obtained via braiding operations.